Differential mode delay (DMD) and effective modal bandwidth (EMB) are the two industry-standardized metrics used to quantify the bandwidth of laser-optimized multimode fiber optic cable (MMF). Laser-optimized fibers are equivalently called OM3 (fiber type A1a.2) and OM4 (fiber type A1a.3). The measurement and calculation procedure for both DMD and EMB is documented in domestic standard TIA-455-220-A and international standard IEC 60793-1-49. TIA-455-220-A and IEC 60793-1-49 are substantially equivalent and are used interchangeably in this disclosure.
The currently standardized algorithms for determining DMD and EMB are adequate for appraising the quantitative amount of modal dispersion of a particular fiber at a particular measurement wavelength. However, they do not correctly address both modal and chromatic dispersion effects, hence EMB cannot accurately be employed in optical communication system models used to estimate limitations and capabilities (e.g., bit-error-rate (BER), supported optical link length). A well known and often referenced system model is the IEEE 10 Gbps link model freely available for download at: http://www.ieee802.org/3/ae/public/adhoc/serial_pmd/documents/10GEPBud3—1—16a.xls which incorrectly estimates the effects due to modal and chromatic dispersion as only additive. Panduit Laboratories has found numerous deviations from the conventional perceived proportional relationship between EMB and system performance (BER). With reference to FIG. 1, it should be noted that the relationship between system performance (BER) and fiber bandwidth is not linear but simply proportional.
U.S. Provisional Patent Application Ser. No. 61/187,137 describes an improved algorithm for calculating the DMD by accounting for the relative shift of the fiber's responses at various radial offsets (magnitude and delay). However, this improvement cannot be advantageously employed to: 1) provide a more accurate bandwidth metric to be used in communication system models; or 2) provide a means that allows modal and chromatic dispersion to be compensated without knowledge of the laser transmitter's fiber-coupled spectral distribution across the fiber core. What is needed is an improved algorithm for calculating the bandwidth of a particular laser transmitter and fiber combination.
For reference, a standardized algorithm for determining the EMB, is summarized as follows in the following six steps and demonstrated herein in Example 1. It is outside the scope of this disclosure to document the comprehensive list of requirements requisite for determining the EMB. Reference is made to TIA-455-220-A for additional information.
In a first step of the standardized algorithm, a DMD measurement apparatus is used to measure the temporal responses of the fiber, U(r,t), to spectrally narrow and temporally short pulses of light with central wavelength, λc, injected into the fiber core at a series of radial offsets, r (typically r=0, 1, 2, 3, . . . , 25 μm for 50 μm MMF fiber). Since U(r,t) is function of wavelength, the final result, EMB, will also be a function of wavelength. Implicit to the DMD and EMB measurement procedure, is the fact that the measurement is only to quantify the effects of modal dispersion at a given wavelength, λc. The temporal response of the launch pulse is R(t).
In a second step of the standardized algorithm, the weighted responses of the fiber, D(r,t,n), is computed with a number, n, of DMD weighting functions, W(r,n). The DMD weighting function(s) is derived from the nearfield data of n laser sources and is employed to emphasize the effects of modal dispersion in the regions of the fiber where the laser source excites the fiber. For additional information on how to determine the weighting function for a particular laser given the laser nearfield, refer to TIA-455-220-A. If the precise bandwidth of a particular fiber and a single laser source (n=1) is to be computed, D(r,t,1), is entirely a function of the nearfield of the single laser source. Alternatively, a large of number of DMD weighting functions, representative of lasers used for a particular application (e.g. 10 GBASE-SR Ethernet), may be employed to provide a range of computed bandwidths. In TIA-455-220-A, ten (n=10) such DMD weighting functions, W(r,10) are employed. Generally the weighted responses of the fiber, D(r,t,n) are given by:D(r,t,n)=U(r,t)W(r,n)  (1)
In a third step of the standardized algorithm, the resultant output pulse, Po(t,n), is computed by summing the weighted response, D(r,t,n) across all r.Po(t,n)=ΣrD(r,t,n)=ΣrU(r,t)W(r,n)  (2)
In a fourth step of the standardized algorithm, the fiber modal dispersion transfer function, Hmd(f,n), is computed and the calculated effective modal bandwidth, EMBc(n) is determined. The fiber modal dispersion transfer functions are determined by deconvolving the launch pulse, R(t), from the resultant output pulse, Po(t,n).Hmd(f,n)=FT{Po(t,n)}/FT{R(t)}  (3)where FT is the Fourier Transform function and the EMBc(n) is defined as the minimum frequency at which point the fiber modal dispersion transfer function, Hmd(f,n), intersects a predetermined threshold value (often times equal to −3 dB). The fiber modal bandwidth may be normalized by fiber length to provide a measure of normalized fiber modal bandwidth (in units of MHz·km).
In TIA-455-220-A, where n=10, the minimum of the ten calculated normalized fiber bandwidths, EMBc(1, 2, 3, . . . , 10) is defined as the minimum EMBc (minEMBc) and is viewed to be the minimum modal bandwidth a particular fiber and a laser transmitter (represented by the ten DMD weighting functions). Furthermore, the minEMBc may be compared against fiber standard specification requirements for modal dispersion. The effective modal bandwidth (EMB) is defined as: EMB=1.13×minEMBc. For OM3 fiber, TIA-492AAAC-A requires minEMBc>1770 MHz·km and for OM4 fiber, TIA-492AAAD will require minEMBc>4159 MHz·km.
In a fifth step of the standardized algorithm, in order to compute the total bandwidth of a fiber and laser source, with non-zero spectral width, the effects of chromatic dispersion are combined with the effects of modal dispersion. In TIA-455-220-A the fiber chromatic dispersion transfer function, Hcd(f) is calculated by multiplying the laser transmitter emitting spectrum, L(λ), and the fiber's wavelength dependence of the time of flight, TOF(λc).Hcd(f)=FT{L(λ)TOF(λc)}  (4)
The measurement procedure described in TIA-455-168-A may be used to measure the fiber's wavelength dependence of the time of flight, TOF(λc). It is expected that the relative time of flight, TOF(λc) will be linear over the relatively small range of wavelengths under consideration (i.e. 840 to 860 nm) and thus linear interpolation may be employed without significant loss of accuracy. Finally, TIA-455-168-A specifies an overfilled launch condition and since it has been found experimentally that the slope of the relative time of flight versus wavelength is not a strong function of radial offset, r, an overfill launch condition may be used. An overfilled launch condition is defined as a launch condition that completely excites all of the supported modes of the fiber.
The measurement procedure described in TIA-455-127-A may be used to measure the laser transmitter emitting spectrum L(λ). It is essential to note, as will be readily appreciated later, that using the prescribed measurement procedure for measuring the laser transmitter emission spectrum, does not provide any information on the spatial location of the laser's various spectral components within the fiber core. This is the reason that the prior art algorithm is not suitable for providing an accurate method of quantifying bandwidth.
In a sixth step of the standardized algorithm, the total fiber transfer functions, Hfiber(f,n), and total calculated bandwidth, CB(n) are computed by combining the effects of modal dispersion and chromatic dispersion with the convolution of Hmd(f,n) and Hcd(f).Hfiber(f)=Hmd(f,n)·Hcd(f)  (5)where CB(n) may be determined in a similar manner as described previously for EMBc(n).
Unfortunately, the standardized algorithm is an oversimplification originating from the loss of spatial resolution of the fiber coupled spectrum within the fiber core. The standardized algorithm assumes a uniform spectral distribution across the fiber core. Without this information, the pulse broadening and time delay (phase shift) effects of chromatic dispersion operate homogeneously across all temporal responses of the fiber and any differential time delay (phase shift) effects across the core resulting from chromatic dispersion are not accounted for. Consequently, when utilizing the standardized algorithm, the magnitudes of modal dispersion and chromatic dispersion effects can only be additive and never subtractive.
It would be desirable to have an improved bandwidth calculation algorithm that can correctly combine both modal and chromatic dispersion effects by accounting for the inhomogeneous nature of fiber coupled wavelengths across the core radius.